Geodesic
Joint universality for periodic Hurwitz zeta-functions
Izvestiya. Mathematics , Tome 72 (2008) no. 4, pp. 741-760

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We obtain a joint universality theorem of Voronin type for systems of periodic Hurwitz zeta-functions with parameters $\alpha_1,\dots,\alpha_r$ such that the system $\{\log(m+\alpha_j):j=1,\dots,r,\ m\in\mathbb{N}_0\}$ is linearly independent over the field of rational numbers. 
@article{IM2_2008_72_4_a5,
     author = {A. Laurin\v{c}ikas},
     title = {Joint universality for periodic {Hurwitz} zeta-functions},
     journal = {Izvestiya. Mathematics },
     pages = {741--760},
     publisher = {mathdoc},
     volume = {72},
     number = {4},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2008_72_4_a5/}
}
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A. Laurinčikas. Joint universality for periodic Hurwitz zeta-functions. Izvestiya. Mathematics , Tome 72 (2008) no. 4, pp. 741-760. http://geodesic.mathdoc.fr/item/IM2_2008_72_4_a5/